I am trying to derive some turbulence model dependencies and I am using Reynolds averaged Navier-Stokes equations. What I am trying to do is to tell Mathematica that OverBar[u] is dependent on x,y,z coordinates and time. However when doing further derivations I would like to avoid writing for example

D[ OverBar[u][x,y,z,t],t]

But rather write just

D[ OverBar[u], t]

But Mathematica should be aware that OverBar is dependent on other variables, because in other case it just writes that D[ OverBar[u],t] is zero.

EDIT: OverBar[u] is not any particular function. It is just time averaged velocity vector which is in general dependent to spatial coordinates and time. There are no any expressions describing it. It is just bare $\bar u$ that I will find using numerical methods. But for now I want to adjust the turbulence model and derive the difference equation, and I do not want to have D[$\bar{u}$,t] output as zero, but rather $\frac{\partial\bar{u}}{\partial{t}}$. Is that possible in Mathematica?

I don't really understand what you mean. And it doesn't work either :(
–
MiserySep 11 '12 at 18:40

@Misery, to tell a function what values it needs to calculate an output, the function either must have those values pre-defined or included as input. So with the simple function I have up in my answer, the arguments x, y, and z are optional. If they are not specified, they assume whatever values the Globalx, y, and z have, either symbolic or numerical
–
kaleSep 11 '12 at 18:44

OK, but still D[u,t] is zero. I think I'll just agree with u[t,x,y,z] :[ Thanks for help :)
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MiserySep 11 '12 at 18:46

@Misery, if you put your function in the Question, I'll adjust the answer to include it.
–
kaleSep 11 '12 at 18:46

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